AP Stats Questions Pls Help!

Question

What is the value of χ² for the two-way table?

A/ B/ C
X	46	21	15
Y	25	32	29
Z	37	23	28

A, B, and C are supposed to be separate columns, sorry the table didn't come out properly.

0.0074

11.7342

12.256

13.4683

13.944

Answer 1

assuming no continuity correction (R applies this by default), the answer is 13.944

The estimated value Eij for each cell is row total * column total / grand total.

For example, the first row total is 82 (46 + 21 + 15), the first column total is 108, and the grand total is 256

Then E₁₁ = 82 * 108/256 =

Let's label the actual values Aij

A₁₁ = 46

Then, to get the Chi squared statistic, we calculate ∑i,j (A_ij - E_ij)^2 / E_ij

For example, our first value is (46 - 34.59375)^2 / 34.59375